The distortion of a knotted curve
Elizabeth Denne
Harvard
April 23, 2007
Abstract: The distortion of a
curve measures the maximum arc/chord length ratio. Gromov showed any
closed curve has distortion at least $\pi/2$ and asked about the
distortion of knots. Here, we used the existence of an essential secant
to show that any nontrivial knot in
space has distortion at least $5\pi/3$; examples show that distortion
under 7.16 suffices to build a trefoil knot.